Note that the fact we used x also y in both the function program and in the command window wasjust a coincidence. In reality it is the name of the file myfunc.m that actually mattered not whatanything in it was called. We could merely as well have made the function

Glance back at the program. All function programs are similar to this one, the necessary elements are:

• Start with the word function.• There are inputs as well as outputs.• The outputs name of the function as well as the inputs must appear in the first line.• The body of the program should assign values to the outputs.

Functions are able to have multiple inputs and/or multiple outputs. Subsequently let’s create a function that has 1input and 3 output variables. Open a new document in addition to type:

function [x2 x3 x4] = mypowers(x)x2 = x.^2;x3 = x.^3;x4 = x.^4;

Save this file as mypowers.m. In the command window we are able to use the results of the program tomake graphs

Write this program into a new document and save it as mygraphs.m. In the command window write:

> x = -1:.1:1;>mygraphs

Note that the program utilized the variable x in its calculations even though x was defined in thecommand window not in the program.

Several people use script programs for routine calculations that would require typing more than onecommand in the command window.

They do this for the reason that correcting mistakes is easier in a programthan in the command window.

Program Comments:

For programs that have extra than a couple of lines it is important to include comments. Commentspermit other people to know what your program does and they as well remind yourself what yourprogram does if you set it aside and come back to it later. It is best to comprise comments not onlyat the top of a program, but as well with each section. In Mat lab anything that comes in a line aftera % is a comment.

For a function program the comments must at least give the purpose, inputs, and outputs. Anappropriately commented version of the function with which we started this section is-

function y = myfunc(x)% Computes the function 2x^2 -3x +1% Input: x -- a number or vector; for a vector the computation is elementwise% Output: y -- a number or vector of the same size as xy = 2*x.^2 - 3*x + 1;

For a script program it is habitually helpful to comprise the name of the program at the beginning. Forillustration:

% mygraphs% plots the graphs of x, x^2, x^3, and x^4% on the interval [-1,1]% fix the domain and evaluation pointsx = -1:.1:1;% calculate powers% x1 is just xx2 = x.^2;x3 = x.^3;x4 = x.^4;% plot each of the graphsplot(x,x,’black’,x,x2,’blue’,x,x3,’green’,x,x4,’red’)

The Mat lab command assists prints the primary block of comments from a file. If we save the above asmygraphs.m and after that do

> help mygraphs

It will print into the command window:

mygraphsplots the graphs of x, x^2, x^3, and x^4on the interval [-1,1]

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